Is there an equation to find roots?

Is there a mathematical equation to find square/cubic/etc. roots of a number?

Any help would be greatly appreciated - this is purely for my own interest. Also, I;m doing the C2 module of AS Maths so I may not understand more complex terms used in an explanation (if any are needed) - apologies in advance for my "ignorance". :)

If you have a logarithm table or if you know one by memory, yes.
Other than that, the only other way I can remember is through a Taylor series expansion. See http://en.wikipedia.org/wiki/Taylor_series
With Taylor series you can only approach the value and it involves hard work and time.
I remember a teacher once saying hand calculators do it with Taylor series. Don't know if it is true.

Today, of course, nobody seems to bother with that stuff, but in my grandfather's day, I am 75, or probably to others in the days of your grandfather's father, they really used that method, or, anyway, they taught it down on the farm.

In those days the multiplication tables went to 12x12 because of the use of the dozen with eggs, etc., and the more difficult things were exercises--I assume, for the better students.

Much of that was taught in a one room schoolhouse--so my grandfather said. And, yes! They had to walk miles through the snow to get to the school in the Winter! Something considered inconceivable today.

Ironically there has been a lot more progress in the last 20years in new ways to do quick arithmatic than the last few hundred.

Before calcualtors people needed to learn arithmetic tricks to make doing sums by hand easier (Feynman's biog lists the fun he had with them) - but the need (and $$$) in making computer calculations faster mean that a lot of tricks for eg. finding roots more efficently have been developed recently. Main markets are cracking codes or for computer game graphics.